It is our purpose here to study the direct collider phenomenology of the
flavon in the \(B_3-L_2\)  model for the first time. The is
expected to have a mass of
order \(M_{Z^\prime }\)  (i.e. the TeV scale) and so may be amenable to
direct production and discovery at high energy colliders. We shall see that
the flavon field
generically mixes with the Higgs field and is therefore bounded by some
electroweak measurements and Higgs searches.
In detail, we wish to make a first estimate of the current and potential
future collider
capabilities of observing the flavon via
flavonstrahlung [1]}LHC \(HZ^\prime \)  production
has been studied in a family universal \(U(1)\)  model in refs. [2]}, [3]}., a process
whose dominant Feynman diagram is depicted
in the right-hand panel of figure REF . Observation of a flavon
would be an important confirmation of the means of
\(U(1)_{B_3-L_2}\)  gauge
symmetry breakdown, since \(U(1)_{B_3-L_2}\)  breaking
could instead be a consequence of the Stueckelberg
mechanism [4]}, which
possesses no explicit flavon field. This
then has implications for the fermion mass puzzle since, for example, the
Froggatt-Nielsen mechanism [5]}, which can explain the
hierarchies between the different families observed in
the measured values of the SM fermion masses, necessarily involves a flavon
field.
